\newproblem{lay:1_5_36}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 1.5.36}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Given $A=\begin{pmatrix}3 & -2 \\ -6 & 4\\12&-8\end{pmatrix}$, find one nontrivial solution of the equation $A\mathbf{x}=\mathbf{0}$.
}
{
  % Solution
	We note that the second and third rows of $A$ are multiples of the first one. So any solution of the form (given by the first row)
	\begin{center}
		$3x_1-2x_2=0$
	\end{center}
	is a solution. In particular $x_1=2$ and $x_2=3$ is a solution. We can check that
	\begin{center}
		$2\begin{pmatrix}3\\-6\\12\end{pmatrix}+3\begin{pmatrix}-2\\4\\-8\end{pmatrix}=\begin{pmatrix}6\\-12\\24\end{pmatrix}+\begin{pmatrix}-6\\12\\-24\end{pmatrix}=
		   \begin{pmatrix}0\\0\\0\end{pmatrix}$
	\end{center}
}
\useproblem{lay:1_5_36}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
